NW 39. Chips Ahoy! Cookies The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and standard deviation 118 chips according to a study by cadets of the US Air Force Academy Source: Brad Warner and Jim Rutledge, Chance 12(1): 10-14, 1999 (a) What is the probability that a randomly selected 18-ounce bag of Chips Ahoy! contains between 1000 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected 18-ounce bag of Chips Ahoy! contains fewer than 1000 chocolate chips? (c) What proportion of 18-ounce bags of Chips Ahoy! contains more than 1200 chocolate chips? (d) What proportion of 18-ounce bags of Chips Ahoy! contains fewer than 1125 chocolate chips? (e) What is the percentile rank of an 18-ounce bag of Chips Ahoy! that contains 1475 chocolate chips? What is the percentile rank of an 18-ounce bag of Chips Ahoy! that contains 1050 chocolate chips?

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!